Using differential equations, please solve for this. If you could draw it also,
ID: 2890961 • Letter: U
Question
Using differential equations, please solve for this. If you could draw it also, that would be appreciated. Thumbs up always given for helpful answers!
Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from tank B into tank A at a rate of 1L/min. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 6L/min. The solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t 0
Explanation / Answer
Solution:
x(t) = Amount of salt in tank A
y(t) = Amount of salt in tank B
tank A:
Rate in 6(0.2) + 3y/100 = 1.2 + 3y/100
Rate out = 4x/100 + 5x/100 = 9x/100
Tank B:
Rate in = 5x/100
Rate out = 3y/100 + 2y/100 = 5y/100
dx/dt = 1.2 + 3y/100 - 9x/100 , x(0) = 0
dy/dt = 5x/100 - 5y/100 , y(0) = 20
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